basic gates 2.1 basic digital logic: application of digital gates using and / or / not ©paul godin...
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Basic Gates 2.1
Basic Digital Logic:Application of Digital Gates
using AND / OR / NOT
©Paul GodinCreated August 2007
Last Update Sept 2013
Basic Gates 2
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Basic Gates 2.2
Timing Diagrams
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Basic Gates 2.3
Timing
◊ Timing diagrams are the best means of comparing the input and output logic values of a digital circuit over time, such as would be found in a functioning circuit.
◊ The output of digital circuit analysis tools such as oscilloscopes and logic analyzers essentially display timing diagrams.
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Basic Gates 2.4
Timing Diagram sample: AND
A
B
Y
A
The output Y is determined by looking at the input A and B
states and comparing them to the truth table for the gate.
Logic 0
B
Y
Logic 1
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Basic Gates 2.5
Timing Diagram sample: OR
A
B
Z
A
B
Z
0 0 0
0
0
0 0
0 01
1
1
1 1
1 1
0 01
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Basic Gates 2.6
Complete the Timing Diagram: Exercise 1
A
B
Z
A
B
Z
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Basic Gates 2.7
Complete the Timing Diagram: Exercise 2
A
B
Z
A
B
Z
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Basic Gates 2.8
Steering Gates
◊ Digital gates can be used to control the flow of one digital signal with another.
1
1
Control
Output
10Signal
1Control
Signal
Output
Animated
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Basic Gates 2.9
Steering Gates
0
1
Control
Output
10Signal
0Control
Signal
Output
0
0
Animated
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Basic Gates 2.10
Combinational Logic
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Basic Gates 2.11
Combinational Logic
◊ Combinational logic describes digital logic circuits that are based on arrays of logic gates. Combinational logic circuits have no retention of states.
◊ Combinational logic circuits can be described with: ◊ English Terms◊ Boolean equations◊ Truth Tables◊ Logic diagrams◊ Timing Diagrams
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Basic Gates 2.12
Combinational Logic Example 1
The circuit below is a combinational logic circuit.
A
B
CY
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Basic Gates 2.13
Combinational Logic Example 1
It can be described in English terms:
A
B
CY
A AND B, OR C equals output Y
A AND B
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Basic Gates 2.14
Combinational Logic Example 1
It can be described using a Boolean equation:
A
B
CY
(A ● B) + C = Y
A ● B
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Basic Gates 2.15
Combinational Logic Example 1
It can be described using a Truth Table:
A
B
CY
A B C Y
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
(A ● B) + C = Y
Only instances where the output of the AND gate = 1
If C is 1, Y is 1
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Basic Gates 2.16
Combinational Logic Example 1
It can be described using a Timing Diagram:
A
B
CY
(A ● B) + C = Y
A
B
C
Y
A B C Y
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
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Basic Gates 2.17
Combinational Logic Example 2
This is a combinational Logic equation:
It can be described as “NOT A AND B AND C equals Y”.It can be drawn this way:
A ● B ● C = Y
ABC
Y
A
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Basic Gates 2.18
Combinational Logic Example 2
The Truth Table and Timing diagram describes its function
A ● B ● C = Y
ABC
Y
A A A’
B C Y
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 1
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 0
A
B
C
Y
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Basic Gates 2.19
Boolean from a Circuit Diagram
◊ A step-by-step process is used to determine the Boolean equation from a circuit diagram.
◊ Begin at the inputs and include the logic expressions while working toward the outputs.
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Basic Gates 2.20
Example 1: Circuit to Boolean
Step 1: AB Step 2: AB Step 3: AB+C
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Basic Gates 2.21
Circuit to Boolean Exercise 1:
Step 1: Step 2:
Convert the following circuit to its Boolean Expression
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Basic Gates 2.22
Circuit to Boolean Exercise 2:
Step 1: Step 2:
Convert the following circuit to its Boolean Expression
Step 3:
Step 4:
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Basic Gates 2.23
Circuit to Boolean Exercise 3:
Step 1:
Step 2:
Convert the following circuit to its Boolean Expression
Step 3:
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Basic Gates 2.24
Circuit to Boolean Exercise 4:
Convert the following circuit to its Boolean Expression
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Basic Gates 2.25
Boolean to Circuit Conversion Example
◊ Take a step-by-step approach when converting from Boolean to a circuit. Work outward from the expression that brings together groupings found within the expression.
◊ Example: Convert (ABC) + BC = Y
YABC
BC
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Basic Gates 2.26
Step 2: One side, ABC
BC
Boolean to Circuit Conversion Example
ABC
Step 3: Other side, BC
BC
ABC
(ABC) + BC = Y
Step 4: Put it all together
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Basic Gates 2.27
Step 5: Tidy up the circuit (inputs on left, outputs on right)
BC
Boolean to Circuit Conversion Example
ABC
BC
ABC(ABC) + BC = Y
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Basic Gates 2.28
Step 6: Common the B and the C inputs
BC
Boolean to Circuit Conversion Example
ABC
ABC(ABC) + BC = Y
Done
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Basic Gates 2.29
Boolean to Circuit Exercise 1:
Draw the circuit whose expression is: (AB)+(CD)
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Basic Gates 2.30
Boolean to Circuit Exercise 2:
Draw the circuit whose expression is: (A+B)•(BC)
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Basic Gates 2.31
Boolean to Circuit Exercise 3:
Draw the circuit whose expression is: (AB) + (AC)
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Basic Gates 2.32
END
©Paul R. Godinprgodin°@ gmail.com